On the other hand, stimulated by experimental progresses, many variations and extensions of the SSH model have been proposed and explored, such as driven SSH model [1]}, [2]}, SSH model with long-range hopping [3]}, [4]}, [5]}, [6]}, Creutz ladder model [7]}, [8]} and extended SSH model [9]}.
One typical extended example is to change the site period of the unit cell from two to
four, thus one can transform the standard SSH model into the
considerably richer SSH4 model with four hopping coefficients [9]}.
The wider parameter space of the SSH4 model is useful for studying
topological properties of system with higher dimensions including synthetic dimension [11]}, [12]}, [13]}, [14]}, [15]}.
The SSH4 model has the chiral symmetry and belongs
to the same topological class of the SSH model, and the winding number
can characterize its band topology [9]}.
With open boundary condition, there exist topological edge states at the boundary
of the system.
For a SSH4 model with infinite sites, the topological trivial and nontrivial phases are determined by
the tunneling ratio.
So far, the single-particle topological characterizations of SSH4 have been investigated clearly [9]}, [18]}, [19]}.
However, to the best of our knowledge, a detailed study of interacting SSH4 model is still lacked.
